Differentials on quotient CDGAs

asked 2023-09-25 10:09:52 +0200

ronno gravatar image

The following code throws a ValueError("The given dictionary does not determine a valid differential"):

A.<x, y, z> = GradedCommutativeAlgebra(QQ, degrees=(2, 3, 4))
AQ = A.quotient(A.ideal(x^3))
E = AQ.cdg_algebra({y: x^2, z: x*y})

It seems the cause is a check if not self(self(i)).is_zero(). Since the error disappears on omitting the z = x*y differential, I presume it's evaluating $d(xy) = x^3$ to be something non-zero, maybe because it is being evaluated in A and not AQ. Is this a bug or am I supposed to define this CDGA in a different way?

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graded_commutative_algebra or GradedCommutativeAlgebra is too long to be a tag, and I couldn't find an alternative. Please feel free to retag.

ronno gravatar imageronno ( 2023-09-25 10:10:46 +0200 )edit

This works fine for me in sage 10.2.beta4. Which version of sage do you use ?

FrédéricC gravatar imageFrédéricC ( 2023-09-25 19:52:51 +0200 )edit

also works fine in sage 10.1 as available on https://sagecell.sagemath.org/

FrédéricC gravatar imageFrédéricC ( 2023-09-25 20:57:20 +0200 )edit

@FredericC 9.5-6 from the Ubuntu repositories, running on WSL.

ronno gravatar imageronno ( 2023-09-26 00:44:08 +0200 )edit

I can confirm that the code works fine on sage 10.1 built from source

ronno gravatar imageronno ( 2023-09-26 04:09:27 +0200 )edit